The present invention relates to a method and an apparatus for determining interpolated intermediate values of a sampled signal, in particular a mobile radio signal.
The interpolated intermediate values of a sampled signal need to be determined wherever only a limited number of sample values of the signal are available as a result of certain limitations. For example, there is a need to calculate interpolated values at different points in the field of computer graphics or the field of digital mobile radio. In particular, an estimate of intermediate values by interpolation is required in the field of mobile radio because only a small number of sample values are available at specific points to be used for analysis of a received signal.
Essentially, the aim of interpolation is to determine a continuous curve or line that passes through a certain number of known points or sample values. The desired intermediate values can then be determined using the line that is now known.
In the following it is assumed that three sample values of the signal for analysis are known, which can be represented by three value pairs (x1, y1), (x2, y2) and (x3, y3), wherexe2x80x94as shown in FIG. 2xe2x80x94the x-values correspond to the sampling instant and the y-values to the associated signal value. The time intervals between each of the sample values may be different.
Given three known sample values or sample pairs, an interpolation can be carried out by using the second-order polynomial y=ax2+bx+c, since the three unknown parameters a, b, and c can be found from the three known value pairs. The following equation system must therefore be solved as efficiently as possible:
y1=ax12+bx1+c
y2=ax22=bx2+c
y3=ax32+bx3+c
The required parameters a, b, and c can thus be found using these three equations, so that then any other intermediate value can be calculated using the general relationship
y=ax2+bx+c.
Because more than three sample values are usually known, for instance the additional value pairs (x4, y4) and (x5, y5) in FIG. 2, curve sections are calculated for every three sample values, which are then pieced together. Here, one curve section is calculated from the sample values (x1, y1), (x2, y2) and (x3, y3), and the other curve section from the sample values (x3, y3), (x4, y4), and (x5, y5)
In order to avoid any discontinuity at the point of intersection (x3, y3) between the two curve sections, the calculation can incorporate the gradient of the curve, which is defined by the first derivative at the point concerned. The gradient m of the second-order polynomial cited above is given in general by
m=2ax+b
The method described above is relatively involved.
U.S. Pat. No. 5,502,662 to Greggain representing the latest prior art, describes an interpolator in which square-law curve interpolation is carried out on a set of three sample points. In order to avoid problems with matching the interpolation curves to adjacent sets of sample points, intermediate values between the sample points are first generated by linear interpolation, and are then used as nodes for the square-law interpolation.
It is accordingly an object of the invention to provide a method and apparatus for determining interpolated intermediate values of a sampled signal that overcomes the hereinafore-mentioned disadvantages of the heretofore-known devices of this general type and that determines interpolated intermediate values of a sampled signal, which enables intermediate values to be determined or calculated by a simple method and apparatus with low hardware complexity.
With the foregoing and other objects in view, there is provided, in accordance with the invention, a method for determining interpolated intermediate values of a sampled signal. The first step of the method is sampling the signal to obtain at least three known samples of the signal forming value pairs (x1, y1), (x2, y2), and (x3, y3) respectively. The next step is determining from the three known sample values the parameters a, b, and c of the second-order polynomial y=ax2+bx+c. The next step is calculating desired intermediate values from the polynomial after determining the parameters of the polynomial, in which the three known sample values are obtained by sampling the signal at constant intervals d. The center sample value is assigned the sampling instant x2=0, and the interval d between the known sample values is normalized to d=1, so that the desired intermediate values are calculated from the second-order polynomial using       a    =                                        y            1                    +                      y            3                          2            -              y        2              ,      xe2x80x83    ⁢      b    =                            y          3                -                  y          1                    2      
and c=y2. The next step is choosing the x-values of the desired intermediate values such that the related y-values of the desired intermediate values represented by the second-order polynomial have only quotients with a power of 2 as denominators.
With the objects of the invention in view, there is also provided an apparatus for determining interpolated intermediate values of a sampled signal according to the previously described method. The apparatus includes a first computation block (1) for calculating the value                     y        1            +              y        3              2    -            y      2        .  
The apparatus also includes a second computation block (2) for Calculating the value                     y        3            -              y        1              2    ,
the x-values of the desired intermediate values whose y-values represented by the polynomial have only quotients with a power of 2 as denominators.
With the objects of the invention in view, there is also provided a use for the above-described method. The use is determining interpolated intermediate values of a sampled digital mobile radio signal.
The present invention relates to the determination or calculation of interpolated intermediate values of a signal in a special situation that arises frequently in the field of mobile communications in particular, so that the solution according to the invention can be applied with almost no loss of generality.
Firstly, according to this invention, it is assumed that the signal is sampled at constant intervals. Secondly, the center sampling instant is defined as x2=0 so that resultant expressions for the unknown parameters a, b and c of the second-order polynomial y=ax2+bx+c to be found, can be evaluated with little effort from the known sample values y1, y2, and y3. Thirdly, the constant interval between the known sample points is normalized with respect to 1, so that the intermediate values are determined in the range [xe2x88x921, 1] about x2=0. The x-values of the desired intermediate values are chosen such that expressions are obtained for the corresponding y-values using the determined polynomial that contain only quotients having denominators that can be represented by a power of 2. This enables a simple, optimized hardware implementation of the interpolator, in which several circuit elements are used more than once, and divisions are not carried out explicitly, but are implemented by shifting the data lines or by renaming the relevant bits, so that no additional hardware is required for this. In addition, multiplications are not carried out as such, but are replaced by far simpler and cleverly selected additions.
The present invention can be used in particular for the analysis of a digital received signal in digital mobile radio systems such as UMTS terminals (Universal Mobile Telecommunication System).
Other features that are considered as characteristic for the invention are set forth in the appended claims.
Although the invention is illustrated and described herein as embodied in a method and apparatus for determining interpolated intermediate values of a sampled signal, it is nevertheless not intended to be limited to the details shown, since various modifications and structural changes may be made therein without departing from the spirit of the invention and within the scope and range of equivalents of the claims.
The construction and method of operation of the invention, however, together with additional objects and advantages thereof will be best understood from the following description of specific embodiments when read in connection with the accompanying drawings.